Chapter 9.2, Problem 2BGP

To determine

To plot: The graph of the equation $y=2{\left(x-1\right)}^2-4$ .

Answer to Problem 2BGP

The graph of the parabola $y=2{\left(x-1\right)}^2-4$ is shown in figure (1).

Explanation of Solution

Given:

The graph of the equation is $y=2{\left(x-1\right)}^2-4$ .

Calculation:

The equation is of the form $y=a{\left(x-h\right)}^2+k$ , where $h=1$ and $k=-4$ . The graph of this equation is the graph of $y=2x^2$ in a translated 1 unit to the right and down 4 units. The vertex is now at $\left(4,5\right)$ .

The graph of the equation $y=2{\left(x-1\right)}^2-4$ is as follows.

  

Figure (1)

Therefore, the graph of the parabola $y=2{\left(x-1\right)}^2-4$ is shown in figure (1).